The invention described herein may be manufactured and used by or for the Government of the United States for all governmental purposes without the payment of any royalty.
The present invention relates generally to mathematically modeling complex physical processes, and more specifically to computationally tractable methods for mathematically modeling film-substrate interactions during formation and growth of thin films.
Simulation of formation and growth of thin films is currently accomplished by use of quantitative models utilizing physics and chemistry theories based on quantum mechanical principles. These xe2x80x9cfirst principlexe2x80x9d approaches require detailed knowledge of the elements involved in the interactions, energies of interaction and parameters associated with the structure and geometry of the substrate and vapor systems. Casting these variables into a form suited to the Hamiltonian required in the solution of the Schrodinger equation governing the atomic behavior of the elements in a system to be modeled is extremely difficult. Solution of the differential equations is time-consuming even on supercomputers. Other approaches such as molecular dynamics require a detailed statement of the equations of motion of the atoms involved. This limits the size of the substrate and vapor atoms to be deposited to a few thousand atoms for practical considerations related to computational time. Monte Carlo methods, while not as demanding in terms of details of each atom, nevertheless require many integrations and iterations on quantitative functions describing the behavior of atoms in the systems. As a result, it too is limited to a few thousand atoms in order to keep the computational times plausible.
Thus it is seen that there is a need for computationally tractable methods for simulating formation and growth of thin films and for simulating other physical processes.
It is, therefore, a principal object of the present invention to provide a computationally tractable method for modeling formation and growth of thin films, particularly as an example of a method that can be applied to any physical process.
It is a feature of the present invention that it facilitates use of computationally complex processes by modeling the processes with a neural network.
It is an advantage of the present invention that it greatly increases the computational speed of a modeling process.
It is another advantage of the present invention that it reduces problem solutions which now require massively parallel computing systems to a single desktop computer.
These and other objects, features and advantages of the present invention will become apparent as the description of certain representative embodiments proceeds.
In accordance with the foregoing principles and objects of the present invention, a new method for modeling dynamic physical systems is described. The unique discovery of the present invention is that a computationally very fast model can be made with a hybrid cellular automaton/neural network where selected cellular automaton algorithms, or other computationally complex computational-subprocesses, are replaced with neural networks where the neural network was trained from a solution set previously generated by the now replaced computationally complex subprocess. In the case of modeling of film-substrate interactions, this approach substantially increases the number of atoms per second that can be modeled.
Accordingly, the present invention is directed to a method for modeling thin-film formation and growth, comprising the steps of modeling the thin-film formation and growth with a cellular automaton system having variable rules for each cell, wherein the rules describe a state change algorithm, creating a training set of solutions for a neural network from the state change algorithm, and using the trained neural network in place of the state change algorithm during operation of the cellular automaton system.
The present invention is also directed to a method for modeling a dynamic process, comprising the steps of creating a model of the dynamic process with a cellular automaton system having variable rules for each cell, wherein the rules are described by an algorithm, creating a training set of solutions for a neural network from the algorithm, training the neural network with the training set of solutions, and using the trained neural network in place of the algorithm during operation of the cellular automaton system.
The present invention is still further directed to a method for modeling a dynamic process, comprising the steps of creating a model of the dynamic process with a computationally complex method, wherein the computationally complex method includes a computationally complex subprocess, creating a training set of solutions for a neural network from the computationally complex subprocess, training a neural network with the training set of solutions, and using the trained neural network in place of the computationally complex subprocess during operation of the computationally complex model.